# In how many ways  can 24 be expressed as the sum of two prime numbers ?

changchengliang | Elementary School Teacher | (Level 2) Adjunct Educator

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By definition, a prime number is a positive integer, excluding '1', that is divisible only by itself and '1'.

For purpose of explanation, allow me to paraphrase the question as:

"Consider m and n being prime numbers.  How many ways can the sum of m and n be equal to 24."

The answer to this question can be derived systematically as follows by listing m (all prime numbers<24 or until it repeats in column for n), then the possibility of n being prime:

"m",  "possible n",  "is n a prime number?"

2,        22,            no

3,        21,            no

5,        19,            yes

7,        17,            yes

11,      13,            yes

Any value of m beyond 11 would have been repeated as n previously.

Hence my answer to this question is:

There are exactly 3 ways of expressing 24 as the sum of two prime numbers.

(140 words)

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